7.

9.

PART C

a. Using Runge-Kutta method of fourth order find y 9-1),y(0.2)and y(0.3) (7 Marks)

given that y'=I+xy; y(O) 52
Discuss the concept of Euler's method in solution of ordinary (5 Marks)
differential equations)

0.

Soive V2u=0 in 04/54; 04/64 given that u(0,y)=0; u(4,y)=8+2y;
a. y(x,0)=0.5x2, y(x,4)=x? with Ax=Ay=1 (10 Marks)
b. Discuss different types of partial differential equations, (2 Marks)
a. Solve V 2u=8x’y?in the square mesh given on the four boundaries (6 Marks)

dividing the square into 16 sub squares of length | unit
b. Apply Picard's method to find the second approximations to the values (6 Marks) of y

and 2 corresponding 1௦ x=O.1 given that

dz
= 2, 602) ۷
− given that and